Question

What is the value of cos $7\frac{1}{2}$ ?

Answer 1

Consider the given function:

$\cos \left(7\frac{1}{2}\right)$

$\cos {15}^0$

$therefore,\cos {15}^0=\cos ({45}^0-{30}^0)$

$\cos {15}^0=\cos {45}^0\cos {30}^0+\sin {45}^0\sin {30}^0$

$=\frac{1}{\sqrt{2}}.\frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}.\frac{1}{2}$

$=\frac{\sqrt{3}}{2\sqrt{2}}+\frac{1}{2\sqrt{2}}$

$=\frac{\sqrt{3}+1}{2\sqrt{2}}$

Hence this is the answer.